Twicing Kernels and a Small Bias Property of Semiparametric Estimators
展示如何构造具有小偏倚性质的半参数估计量，证明基于双核估计的半参数估计量具有该性质，并通过蒙特卡洛实验发现其均方误差更小且对带宽不敏感。
The purpose of this note is to show how semiparametric estimators with a small bias property can be constructed. The small bias property (SBP) of a semiparametric estimator is that its bias converges to zero faster than the pointwise and integrated bias of the nonparametric estimator on which it is based. We show that semiparametric estimators based on twicing kernels have the SBP. We also show that semiparametric estimators where nonparametric kernel estimation does not affect the asymptotic variance have the SBP. In addition we discuss an interpretation of series and sieve estimators as idempotent transformations of the empirical distribution that helps explain the known result that they lead to the SBP. In Monte Carlo experiments we find that estimators with the SBP have mean-square error that is smaller and less sensitive to bandwidth than those that do not have the SBP. Copyright The Econometric Society 2004.